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Reduction approach and three types of multi-soliton solutions of the shifted nonlocal mKdV equation

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Abstract

In this paper, a reduction approach is proposed for a shifted nonlocal mKdV equation, from which we obtain its three types of multi-soliton solutions. Specifically, we proceed with the general N-soliton solution of an AKNS “\((q,r)\ \mathrm{system}\)” in the form of Riemann–Hilbert formulation. Then, by imposing suitable parameter constraints such that the shifted nonlocal symmetry reduction condition is fulfilled, we succeed to reduce the N-soliton solution of the AKNS “\((q,r)\ \mathrm{system}\)” to three types of multi-soliton solutions of the shifted nonlocal mKdV equation, which are classified according to the spectrum configurations. Moreover, several specific solutions are theoretically and graphically investigated. The proposed reduction approach paves a way for calculating multi-soliton solutions of the shifted nonlocal mKdV equation, which does not involve complicated spectral analysis of the Lax pair of the equation.

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Acknowledgements

The author expresses sincere thanks to the editor and the anonymous referees for their valuable suggestions. The author would also like to thank the support by the Collaborative Innovation Center for Aviation Economy Development of Henan Province.

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  1. School of Science, Zhengzhou University of Aeronautics, Zhengzhou, 450046, Henan, People’s Republic of China

    Jianping Wu

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Wu, J. Reduction approach and three types of multi-soliton solutions of the shifted nonlocal mKdV equation. Nonlinear Dyn 109, 3017–3027 (2022). https://doi.org/10.1007/s11071-022-07566-5

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